You're completely right.
Basically, you know the Capacitance, and you're giving the function of current with respect to time. Since you can just Integrate your I function with respect to t.
Just use a simple u substitution so that
From there, you can just integrate the function as
and you will end up with the answer
Change your back into
Once you plug in your limits of 0 and 2 you will get
You know that so your final result should be